Abstract (inglese)

This thesis focuses on the development and the application of a computational methodology, based on a molecular ﬁeld theory and atomistic modelling, to connect dielectric and elastic properties of nematic liquid crystals to the structure of the constituent molecules.

Chapter 1 is a general introduction on the subject of the thesis. Firstly, the problem of the connection between materials properties and structure of the molecular constituents is introduced, with special reference to the case of liquid crystals, and the object of this work is presented. The main features of liquid crystals are then recalled, considering in particular the elastic and dielectric properties, investigated in this thesis, which are
directly involved in the electro-optical behaviour. We also show the molecular systems to which the theoretical- computational methodology developed here has been applied. These have the common structure of two mesogenic, rather rigid units, connected by a ﬂexible spacer. For these reasons they are called ‘dimers’. These mesogens have several
reasons of interest: their liquid crystal properties are very sensitive to changes in the molecular structure and exhibit some unusual and unexplained features. Therefore they can been devised as a benchmark for molecular modelling of liquid crystals.

In chapter 2 the theoretical framework is presented. After a review of the state of the art of the computational methods for the study of liquid crystals, we present the molecular ﬁeld approach used in this thesis, which is based on the ‘Surface Interaction’ (SI) model. Herein, the relation between molecular and mesoscale level is introduced
through the assumption that each element of the molecular surface tends to align to the nematic director. A realistic account of the molecular structure is made possible by the use of a surface generated from atomic coordinates. We report the molecular expressions obtained in this framework for the ordering, thermodynamic, ﬂexoelectric and dielectric
properties of nematic liquid crystals. Given the role played by the molecular ﬂexibility, special attention is devoted to the conformational degrees of freedom. Two different ways are proposed for its inclusion in the model: the Rotational Isomeric State (RIS) approximation, in which only the molecular geometries corresponding to the minima of
the torsional potential are considered, or the Monte Carlo (MC) sampling of torsional angles.

In chapter 3 we derive molecular expressions for the bulk and surfacelike elastic constants of nematics, within the framework of the SI model. This requires extensive use of tensor calculus; after some lengthy algebra, simple expressions are obtained, by exploiting the symmetry of the undeformed nematic phase. From the point of view of the theoret-
ical development, this is the main result of the present thesis. The elastic constants can be calculated as a function of the orientational order, without any free parameter, at low computational cost. It enables us to investigate the role of molecular features and to explore how changes at the atomic level can be conveyed into changes in elastic behaviour, on a quite diﬀerent length-scale. Therefore it can shed light on the origin, still
poorly understood, of the diﬀerent elasticity of mesogens with diﬀerent structure. The predictive ability of this method makes it potentially useful for the synthetic design of tailored mesogens: the elastic constants can be easily calculated, if the molecular structure is known. We also derive molecular expressions for the surfacelike elastic constants
of nematics. The surface elasticity of nematics has been a subject of intense theoretical and experimental investigation and no consensus has been reached; our analysis can be seen as a preliminary exploration of this problem, which deserves further investigation in the future, and we hope that our atomistic level approach can provide some new insight.
In chapter 5 the elastic behaviour of three typical liquid crystals mesogens (PAA, 5CB, 8CB) is investigated, using the molecular ﬁeld theory presented in Chapter 3. These have been chosen as representative cases because of their diﬀerent elasticity, despite the
structural similarity. The availability of experimental data allows us to assess the quality of the theoretical predictions. We show that the observed temperature dependence of the splay, twist and bend elastic moduli can be traced back to diﬀerences, even not dramatic,
in molecular shape. Our calculations also highlight the importance of the ﬂexibility of mesogens, which was generally ignored by previous theories: in view of their diﬀerent shape, conformers are shown to give diﬀerent contributions to the elastic moduli. The key role of deviations from a rod-like shape, which is generally assumed by models of mesogens,
emerges from the calculations. The bend elastic constant is shown to be particularly sensitive to molecular bending; it can range from high values for rod-like conformers, to low and even negative values for bent conformers of a given compound. These ﬁndings could have important implications for bent-core mesogens, which are presently the object
of intense investigation because of their unusual and attractive properties. We also report the surfacelike elastic constants of PAA, 5CB, 8CB, whose experimental determination is controversial; we have found that these are generally smaller than the bulk elastic moduli and even more sensitive to changes in molecular shape. The results obtained for the LC dimers, taking into account the conformational freedom at the RIS level, are reported in chapter 6. A full overview is provided, comprising
order parameters, properties at the nematic-isotropic transition, dielectric permittivity, elastic and ﬂexoelastic moduli. The molecular model enables us to reach an unprecedented insight into the origin of not yet explained experimental ﬁndings, and to predict behaviours not yet probed by experiment. Particularly interesting are the results obtained
for the ﬂexoelectric and elastic properties of the LC dimers. The common view, which gives electric and steric dipoles the main responsibility for the ﬂexoelectric properties, cannot explain recent experimental ﬁndings for LC dimers; our results single out the importance of taking into account the whole distribution of charges and the real molecular
shape. Experimental data are available for the splay elastic constants of dimers [Tsvetkov et al, Mol. Cryst. Liq. Cryst.: 331:1901, 1999]: we correctly predict not only magnitude of the elastic constants, but also their dependence on the length of the ﬂexible spacer. No comparison with experiment is possible for the twist and bend elastic moduli; however
our results appear very promising, in relation to some intriguing phenomena which have been recently reported for LC dimers [Coles et al, Nature, 436:997, 2005] and bent-core LCs [G¨rtz et al, Soft Matter, 5:463, 2009].

In chapter 7 we investigate whether the small amplitude ﬂuctuations around the minima of the torsional potential, which are neglected by the RIS approximation, can aﬀect the elastic and dielectric properties of LC dimers. To this purpose, we have performed calculations with MC sampling of the torsional angles. We show that small amplitude ﬂuctuations do play a role for those properties which are particularly sensitive to the balance between elongated and bent conformations; these comprise the bend elasticity and ﬂexoelectricity. Signiﬁcant, though less subtle eﬀects of torsional oscillations are also found for the dielectric permittivity, when some of the torsional angles are characterised
by relatively low barriers between the minima. In this ﬁnal chapter, collecting all the results obtained for LC dimers, we are able to provide a complete explanation for the experiments performed by Coles and colleagues [Coles et al, J. Mater. Chem.,11:2709, 2001; Morris et al, Phys. Rev. E, 75:041701,2007], which simultaneously involve elastic
and ﬂexoelectric properties.